On the differential spectrum of a differentially 3-uniform power function |
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| Institution: | 1. School of Mathematics, Shandong University, Jinan, 250100, China;2. Hubei Key Laboratory of Applied Mathematics, School of Cyber Science and Technology, Hubei University, Wuhan, 430062, China;3. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China;1. School of Mathematical Sciences, Hebei Workstation for Foreign Academicians, Hebei Normal University, Shijiazhuang 050024, PR China;2. Chelyabinsk State University, 129 Bratiev Kashirinykh st., Chelyabinsk 454021, Russia;3. Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada;1. College of Science, National University of Defense Technology, Changsha, 410073, China;2. Hunan Engineering Research Center of Commercial Cryptography Theory and Technology Innovation, Changsha 410073, China;1. Department of Mathematics and Computer Science, Santa Clara University, 500 El Camino Real, 95053, USA;2. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China;2. School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, China;3. Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China;4. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;5. School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, China |
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| Abstract: | In this paper, we investigate the cardinality of the intersection of four particular cyclotomic classes of order two over the finite field with characteristic 5 by making most use of the cyclotomic numbers of orders two and four. As a consequence, a class of power functions over is shown to be differentially 3-uniform and its differential spectrum is also completely determined. |
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| Keywords: | Power function Differential spectrum Cyclotomic number |
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